Min–max and min–max regret versions of combinatorial optimization problems: A survey

Min–max and min–max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min–max and min–max regret versions of some combinatorial optimization problems: shortest path, spannin...

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Bibliographic Details
Published in:European journal of operational research Vol. 197; no. 2; pp. 427 - 438
Main Authors: Aissi, Hassene, Bazgan, Cristina, Vanderpooten, Daniel
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2009
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Approximation
Assignment problem
Combinatorial optimization
Complexity
Exact sciences and technology
Flows in networks. Combinatorial problems
Knapsack problem
Min-max Min-max regret Combinatorial optimization Complexity Approximation Robustness
Min–max
Min–max regret
Operational research and scientific management
Operational research. Management science
Optimization algorithms
Robustness
Shortest path algorithms
Studies
Robustness
Min–max
Min–max regret
Approximation
Combinatorial optimization
Complexity
Spanning tree
Minimax method
NP hard problem
Shortest path
Min-max
Knapsack problem
Min-max regret
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:Min–max and min–max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min–max and min–max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min s– t cut, knapsack. Since most of these problems are NP-hard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2008.09.012